Lucile Randon, who took the name of Sister Andre in 1944, tested positive for coronavirus on 16 January but didn't develop any symptoms.
She told local media she "didn't even realise I had it".
She isolated herself separately from other residents in her retirement home in Toulon, southern France, but is now considered fully recovered.
Sister Andre, who is blind and uses a wheelchair, is now looking forward to celebrating her birthday on Thursday - although she is going to mark the occasion with a smaller group of residents than usual.
"She has been very lucky," David Tavella, spokesman for the Sainte Catherine Labouré retirement home, said.
He told Var Matin newspaper: "She didn't ask me about her health, but about her habits. For example, she wanted to know if meal or bedtime schedules would change.
"She showed no fear of the disease. On the other hand, she was very concerned about the other residents."
Sister Andre was born on 11 February 1904. As well as being Europe's oldest person, she is also the second-oldest living person in the world, according to the Gerontology Research Group's (GRG) World Supercentenarian Rankings List.
When asked by French broadcaster BFM if she was scared of having Covid, Sister Andre said: "No, I wasn't scared, because I wasn't scared to die.
"I'm happy to be with you, but I would wish to be somewhere else - to join my big brother, and my grandfather and my grandmother."